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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Evolutionary Dynamics of a Single-Species Population Model with Multiple Delays in a Polluted Environment

Discontinuity, Nonlinearity, and Complexity 9(3) (2020) 433--459 | DOI:10.5890/DNC.2020.09.007

Ashok Mondal$^{1}$, A. K. Pal$^{2}$, G. P. Samanta$^{1}$

$^{1}$ Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah - 711 103, India

$^{2}$ Department of Mathematics, S. A. Jaipuria College, Kolkata-700005, India

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Abstract

In this work, evolutionary dynamical behaviour of a single-species population model in a polluted environment has been analyzed. This model system describes the effect of toxicant on a single-species population. Two discrete time delays have been incorporated for proper description. Important mathematical characteristics of the proposed model such as positivity, boundedness, stability and Hopf-bifurcation for all possible combinations of both the delays at the interior equilibriumpoint of the model system have been discussed. It is observed that increase amount of delay may lead to the change of stable behaviour of stationary points through the creation of limit cycles and higher periodic oscillations. Furthermore, it is reported that Hopf-bifurcations may also occur around stationary points for corresponding non-delayed system. Various numerical simulations are performed to validate analytical findings.

Acknowledgments

The authors are grateful to the anonymous referees and the Editor Dr. Dimitri Volchenkov, DSc, for their careful reading, valuable comments and helpful suggestions, which have helped them to improve the presentation of this work significantly. The first author (Ashok Mondal) is thankful to the University Grants Commission, India for providing SRF (RGNF).

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